Modifying the shape of FB-spline curves

FB-spline curves are the unification of recently developed trigonometric CB-spline and hyperbolic HB-spline curves, including the classical B-spline curves. These generalized curves overcome some restrictions of B-spline curves and allow to design some important curves like helix, cycloids or catenary. Their properties, however, have been studied only theoretically. In this paper practical shape modification algorithms of FB-spline curves are discussed, including the geometrical effects of the alteration of shape parameters, which are essential from the users’ point of view.     

Examination of a portable99Mo/99mTc isotope generator /SUBLITECHR/

Three SUBLITECH^R technetium generators were milked and generator products were tested for 5 d. Radionuclidic and radiochemical purity, pH of sodium pertechnetate solutions were -emitting impurities and pirogenity were not carried out. We can summarize that generators were running efficiently during our test period and in all cases the pertechnetate produced met the requirements of the European Pharmacopoeia.     

The thermal decomposition of hydro-carbons. Part 1. n-alkanes (C≥5)

The pyrolysis of the long (C≥5) chain n-alkanes is reviewed with emphasis on the radical chain mechanism and on the reactions of the intermediate alkyl radicals. The effects of the experimental conditions and conversion on the types and distributions of the final products are also evaluated. The Arrhenius rate parameters are summarized for both the elementary steps and the overall decomposition reactions.     

7-Methylguanine nucleotides and their structural analogues; protolytic equilibria, complexing with magnesium (II) ion and kinetics for alkaline opening of the imidazole ring

First-order rate constants for the alkaline opening of the imidazole ring of several 7-methylguanine nucleotides and their structural analogues were determined. The results obtained suggested that intramolecular interaction between the negatively charged 5'-phosphate group and the positively charged imidazole ring markedly retard the attack of hydroxide ion on the C8 atom of the 7-methylguanine ring. In contrast, hardly any influence on the acidities of the interacting base and phosphate moieties was detectable. No effect on the complexing of the phosphate group with magnesium(II) ion could be detected.     

A generalization of carathéodory''s theorem

The following theorem is proved. If the sets and a εⁿ⁺¹_i=1 conv V_i, then there exist elements v_i ε V_i (i=1…,n+1) such that a ε conv{v₁,…,v_n+1}. This is generalization of Carathéodory's theorem. By applying this and similar results some open questions are answered.     

Identification of novel chiral aluminium containing oxonium cations in the enantioselective hydrogenation of ethyl pyruvate catalyzed using cinchonidine modified Pt-alumina in acetic acid

Summary The first identification of aluminium containing oxonium cations having chiral atomic groups is described which may play a role in enantioselective hydrogenation of ethyl pyruvate using Pt-alumina catalyst in AcOH. The structure these cations at m/z = 509 and m/z = 567 is: [O{Al(OAc)₂}₂Al(OPy.OLt)]⁺ and [O(AlOAc.OLt)₂Al(OPy)₂]⁺     

Modeling rate-controlling solvent effects. The pericyclic meisenheimer rearrangement of N-propargylmorpholine N-oxide

The activation parameters of the pericyclic Meisenheimer rearrangement and a competitive rearrangement of N-propargylmorpholine N-oxide were determined by experimental and computational methods. A number of aprotic and protic solvents of different polarities and hydrogen bond-forming abilities and the roles of electron-pair acceptor additives were investigated. The reaction kinetics were followed by means of NMR. In protic solvents, isotope-labeling experiments revealed a novel inverse secondary kinetic isotope effect (k(H)/k(D) about 0.8) for the rate-determining cyclization step, probably occurring because of a C(sp) --> C(sp(2)) change in hybridization at the reaction center. In molecular computations at the B3LYP/6-31++G(d,p) level of theory, implicit, explicit, and joint explicit-implicit solvent models were used. The explicit-implicit model and molecular dynamic simulations gave the most accurate results. The components of the rate-controlling solvent effect are discussed, and general equations are proposed for accurate prediction of the solvent-dependent activation parameters.     

Sum-free sets in abelian groups

An IP system is a functionn taking finite subsets ofN to a commutative, additive group Ω satisfyingn(α∪β)=n(α)+n(β) whenever α∩β=ø. In an extension of their Szemerédi theorem for finitely many commuting measure preserving transformations, Furstenberg and Katznelson showed that ifS _i ,1≤i≤k, are IP systems into a commutative (possibly infinitely generated) group Ω of measure preserving transformations of a probability space (X, B, μ, andA∈B with μ(A)>0, then for some ø≠α one has μ(? _i=1 ^k S _i({α})A>0). We extend this to so-called FVIP systems, which are polynomial analogs of IP systems, thereby generalizing as well joint work by the author and V. Bergelson concerning special FVIP systems of the formS(α)=T(p(n(α))), wherep:Z ^t →Z ^d is a polynomial vanishing at zero,T is a measure preservingZ ^d action andn is an IP system intoZ ^t . The primary novelty here is potential infinite generation of the underlying group action, however there are new applications inZ ^d as well, for example multiple recurrence along a wide class ofgeneralized polynomials (very roughly, functions built out of regular polynomials by iterated use of the greatest integer function).